This Has Always Bugged Me
Why is it so important that her parents don't find out?
I mean, they can't really do anything about it. They're out of the country most of the time, so they can't exert any true control over Megumi's capability to kick ass. And if they get mad about it, so what? Megumi didn't want this to happen to her, yet she's adapted splendidly, and is helping out the police? Why shouldn't they feel proud of her?

@YRPOtaku169: Superheroes have secret identies so that their friends and family don't get in harm's way. Superheroes have a lot of enemies who wouldn't hesitate to try to get to them through their loved ones.

If Megumi's parents found out, it wouldn't be the end of the world, but it wouldn't be good either; there'd be a greater chance her secret would slip. Also, what would YOUR parents think if they discovered you were risking your life on a semi-regular basis to fight crime? As a teenager?

...Yes I know she's superpowered with cartoon invulnerability, but if the webcomic has shown us anything so far, that's no guarantee of her safety. They'd probably be upset at the Goddess twins for putting their daughter in danger (and, to a certain extent, rightfully so).